Traveling wavefronts of a delayed temporally discrete reaction-diffusion equation

Abstract

With the growth of a single species with age structure on an unbounded domain as a prototype, we derive a delayed temporally discrete reaction-diffusion equation. The main result is on the existence of traveling wavefronts of the equation. We first transform the problem into that on the existence of fixed points of a mapping. Then by successfully constructing a pair of upper and lower solutions, we establish the existence of traveling wavefronts by applying the upper-lower solution method.